We investigate the projected minimum constraints set by next-generation gravitational wave detectors Einstein Telescope and LISA on the abundance of primordial black holes relative to dark matter from both resolvable mergers and the stochastic gravitational wave background (SGWB) for extended primordial black hole mass distributions. We consider broad power law distributions for a range of negative and positive exponents γ and top-hat distributions (with γ = 0) and use the IMRPhenomXAS waveforms to simulate binary sources up to mass ratios qmax = 1000 and redshifts z = 300. Our results suggest that accounting for extended mass distributions have the most apparent impact when considering mergers at high redshifts z > 30, for which the constraint curves have broader mass windows and shift to higher abundances compared to when a monochromatic distribution is assumed; on the other hand, constraints from low-redshift mergers and the SGWB do not change much with the assumed mass distribution. At high redshifts, astrophysical black holes are not expected to contribute significantly, providing possible smoking-gun evidence for PBHs. Constraints derived from LISA and ET observations would complement each other by probing different PBH mass windows and this holds for the extended mass distributions studied.

中文翻译：

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扩展质量分布的原始黑洞丰度的投影引力波约束


我们研究了下一代引力波探测器 Einstein Telescope 和 LISA 对原始黑洞相对于暗物质丰度的预测最小约束，这些约束来自可分辨合并和扩展原始黑洞质量分布的随机引力波背景 （SGWB）。我们考虑了一系列负指数和正指数 γ 分布和顶帽分布（γ = 0）的广泛幂律分布，并使用 IMRPhenomXAS 波形来模拟质量比高达 qmax = 1000 和红移 z = 300 的二进制源。我们的结果表明，在考虑高红移 z > 30 处的合并时，考虑扩展质量分布的影响最明显，与假设单色分布时相比，约束曲线具有更宽的质量窗口并转移到更高的丰度;另一方面，来自低红移合并和 SGWB 的约束与假设的质量分布没有太大变化。在高红移下，预计天体物理黑洞不会做出重大贡献，从而为 PBH 提供可能的枪式证据。从 LISA 和 ET 观测得出的约束将通过探测不同的 PBH 质量窗口来相互补充，这适用于所研究的扩展质量分布。